DC-to-DC converters capable of discontinuous conduction mode, and associated methods

ABSTRACT

A method for discontinuous conduction mode operation of a multi-phase DC-to-DC converter includes (a) forward biasing a first inductor being magnetically coupled to a second inductor, (b) reverse biasing the first inductor after forward biasing the first inductor, (c) while reverse biasing the first inductor and before magnitude of current through the first inductor falls to zero, forward biasing the second inductor.

RELATED APPLICATIONS

The present Application claims benefit of priority to U.S. ProvisionalPatent Application Ser. No. 62/507,066, filed on May 16, 2017, which isincorporated herein by reference.

BACKGROUND

It is known to electrically couple multiple DC-to-DC sub-converters inparallel to increase DC-to-DC converter capacity and/or to improveDC-to-DC converter performance. One type of DC-to-DC converter withmultiple switching sub-converters is a “multi-phase” DC-to-DC converter,where the sub-converters, which are often referred to as “phases,”switch out-of-phase with respect to each other in at least someoperating modes. Such out-of-phase switching results in ripple currentcancellation at the converter output filter and allows the multi-phaseDC-to-DC converter to have a better transient response than an otherwisesimilar single-phase DC-to-DC converter.

A multi-phase DC-to-DC converter's performance can be improved bymagnetically coupling the energy storage inductors of two or morephases. Such magnetic coupling results in ripple current cancellation inthe inductors and increases ripple switching frequency, therebyimproving converter transient response, reducing input and outputfiltering requirements, and/or improving converter efficiency, relativeto an otherwise identical converter without magnetically coupledinductors.

Two or more magnetically coupled inductors are often collectivelyreferred to as a “coupled inductor” and have associated leakageinductance and magnetizing inductance values. Magnetizing inductance isassociated with magnetic coupling between windings; thus, the larger themagnetizing inductance, the stronger the magnetic coupling betweenwindings. Leakage inductance, on the other hand, is associated withenergy storage. Thus, the larger the leakage inductance, the more energystored in the inductor. Leakage inductance results from leakage magneticflux, which is magnetic flux generated by current flowing through onewinding of the coupled inductor that is not coupled to the otherwindings of the inductor.

A DC-to-DC converter including one or more inductors may operate in acontinuous conduction mode (CCM) or in a discontinuous conduction mode(DCM). CCM is characterized by current through the one or more inductorscontinuously flowing, such that the current is always greater than zero.DCM, in contrast, is characterized by current through the one or moreinductors remaining at zero for a portion of each switching period. CCMpromotes fast transient response and high heavy-load efficiency.Consequently, DC-to-DC converters are commonly designed to operate inCCM at heavy loads. However, CCM can be relatively inefficient at lightloads. Therefore, many DC-to-DC converters are designed operate in DCMunder light loads.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a two-phase DC-to-DC converter capable of DCM andincluding a coupled inductor, according to an embodiment.

FIG. 2 illustrates CCM of the FIG. 1 DC-to-DC converter.

FIG. 3 illustrates DCM of the FIG. 2 DC-to-DC converter.

FIG. 4 illustrates DCM of a two-phase DC-to-DC converter with only oneenergy transfer pulse per period.

FIG. 5 illustrates DCM of an alternate embodiment of the FIG. 1 DC-to-DCconverter.

FIG. 6 illustrates DCM of another alternate embodiment of the FIG. 1DC-to-DC converter.

FIG. 7 illustrates DCM of yet another alternate embodiment of the FIG. 1DC-to-DC converter.

FIG. 8 illustrates a four-phase DC-to-DC converter capable of DCM andincluding a coupled inductor, according to an embodiment.

FIG. 9 illustrates DCM of the FIG. 8 DC-to-DC converter.

FIG. 10 illustrates DCM of an alternate embodiment of the FIG. 8DC-to-DC converter.

FIG. 11 illustrates magnetic coupling of the alternate embodiment of theFIG. 10.

FIG. 12 illustrates DCM of another alternate embodiment of the FIG. 8DC-to-DC converter.

FIG. 13 illustrates magnetic coupling of the alternate embodiment ofFIG. 12.

FIG. 14 illustrates a method for discontinuous conduction mode operationof a multi-phase DC-to-DC converter, according to an embodiment.

DETAILED DESCRIPTION OF THE EMBODIMENTS

While there are significant benefits to using coupled inductors inmulti-phase DC-to-DC converters, it is difficult to obtain highefficiency under light-load conditions using conventional techniques. Inparticular, Applicant has determined that the ratio of transferred powerto magnetic core losses is typically low during DCM, resulting in lowefficiency. Accordingly, Applicant has developed DC-to-DC converterswith coupled inductors that are capable of transferring more powerduring DCM than conventional DC-to-DC converters, thereby promoting highefficiency under light-load conditions.

For example, FIG. 1 illustrates a two-phase DC-to-DC converter 100having a buck topology and capable of DCM. DC-to-DC converter 100includes an input port 102, an output port 104, a first switchingcircuit 106, a second switching circuit 108, a first inductor 110, asecond inductor 112, an input capacitor 114, an output capacitor 116,and a controller 118. First inductor 110 is magnetically coupled tosecond inductor 112 to collectively form a coupled inductor 120, whereeach inductor 110, 112 has a respective leakage inductance. Coupledinductor 120 also has a magnetizing inductance associated with magneticcoupling of first and second inductors 110, 112. First inductor 110 iselectrically connected between a first switching node V_(x1) and acommon output node V_(o), and second inductor 112 is electricallyconnected between a second switching node V_(x2) and common output nodeV_(o). Current through each of first inductor 110 and second inductor112 is summed at common output node V_(o), and output capacitor 116capacitively filters common output node V_(o).

First switching circuit 106 is electrically connected to first switchingnode V_(x1), and second switching circuit 108 is electrically connectedto second switching node V_(x2). Each switching circuit 106 and 108 iselectrically connected to input port 102, which is in turn electricallyconnected to an input node V_(in). An electric power source 124 iselectrically connected between input node V_(in) and a reference node126. Output port 104 is electrically connected to output node V_(o).Input capacitor 114 is electrically connected between input node V_(in)and reference node 126, and output capacitor 116 is electricallyconnected between output node V_(o) and reference node 126. Eachswitching circuit 106, 108 and its respective inductor 110, 112 arecollectively referred to as a “phase” 122 of the converter. Thus,DC-to-DC converter 100 has two phases. In this document, specificinstances of an item may be referred to by use of a numeral inparentheses (e.g., phase 122(1)) while numerals without parenthesesrefer to any such item (e.g., phases 122).

Each switching circuit 106, 108 includes a control switching device 128that alternately switches between its conductive and non-conductivestates under the command of controller 118. Switching devices 128 areconsidered “control” switching devices because magnitude of converteroutput voltage, i.e. voltage at output port 104, is a function of dutycycle of switching devices 128. Each switching circuit 106, 108 furtherincludes a freewheeling switching device 130 adapted to provide a pathfor current through its respective inductor 110, 112 when the controlswitching device 128 of the switching circuit transitions from itsconductive to non-conductive state. In the context of this disclosure, aswitching device includes, but is not limited to, a bipolar junctiontransistor, a field effect transistor (e.g., a N-channel or P-channelmetal oxide semiconductor field effect transistor, a junction fieldeffect transistor, a metal semiconductor field effect transistor), aninsulated gate bipolar junction transistor, a thyristor, or a siliconcontrolled rectifier.

Controller 118 causes each switching circuit 106, 108 to repeatedlyswitch its respective inductor 110, 112 between input node V_(in) andreference node 126, thereby repeatedly forward biasing and reversebiasing its respective inductor, to transfer power from electric powersource 124 to a load (not shown) electrically connected to output port104. In this document, an inductor is “forward biased” when theinductor's respective control switching device is operating in itsconductive state and the inductor's respective freewheeling switchingdevice is operating in its non-conductive state. For example, inductor110 is forward biased when control switching device 128(1) is operatingin its conductive state and freewheeling switching device 130(1) isoperating in its non-conductive state. Conversely, an inductor is“reversed biased” in this document when the inductor's respectivecontrol switching device is operating in its non-conductive state andwhen the inductor's respective freewheeling switching device isoperating in its conductive state. For example, inductor 110 is reversebiased when control switching device 128(1) is operating in itsnon-conductive state and freewheeling switching device 130(1) isoperating in its conductive state. Additionally, each switching circuit106, 108 is capable of operating in a high impedance state, and therebyelectrically isolating its respective inductor, by operating each of itscontrol switching device 128 and its freewheeling switching device 130in their non-conductive states. For example, inductor 110 iselectrically isolated when both of control switching device 128(1) andfreewheeling switching device 130(1) are operating in their respectivenon-conductive states.

Controller 118 generates signals 132, 134, 136, 138 to control switchingdevices 128(1), 130(1), 128(2), 130(2), respectively. When a signal 132,134, 136, 138 is asserted, its respective switching device 128(1),130(1), 128(2), 132(2) is in its conductive state. Conversely, when asignal 132, 134, 136, 138 is de-asserted, its respective switchingdevice 128(1), 130(1), 128(2), 132(2) is in its non-conductive state.Connections between signals 132, 134, 136, 138 and their respectiveswitching devices are not shown in FIG. 1 to promote illustrativeclarity. Controller 118 is optionally configured to control switchingcircuits 106, 108 to regulate one or more parameters of two-phaseDC-to-DC converter 100, such voltage at output port 104 and/or currentthrough output port 104.

Controller 118 typically causes switching circuits 106, 108 to switch ata relatively high frequency, optionally at 100 kilohertz or greater, topromote low ripple current magnitude and fast transient response, aswell as to ensure that switching induced noise is at a frequency abovethat perceivable by humans. Additionally, in certain embodiments,controller 118 causes switching circuits 106, 108 to switch out-of-phasewith respect to each other in CCM.

Controller 118 includes a processor 140, a memory 142, and interfacecircuitry 144. Processor 140 executes instructions 146, in the form offirmware or software stored in memory 142, to control DC-to-DC converter100, such as to control switching circuits 106, 108. Interface circuitry144 electrically interfaces processor 140 with other circuitry, such asswitching circuits 106, 108. For example, in some embodiments, interfacecircuitry 144 includes level shifting circuitry for converting signalsfrom processor 140 to signals 132, 134, 136, 138 in a form suitable fordriving control switching devices 128 and freewheeling switching devices130. In certain embodiments, controller 118 is partially or fullyimplemented as an integrated circuit, optionally further includingswitching circuits 106, 108. In some alternate embodiments, processor140 and memory 142 are replaced with, or supplemented by, analog and/ordigital electronic circuitry.

Controller 118 is configured to operate DC-to-DC converter 100 in atleast two modes, i.e., CCM and DCM. FIG. 2 is a graph 200 illustratingoperation in CCM. Vertical axis 202 represents magnitude, and horizontalaxis 204 represents time. Graph 200 includes curves representing current206 through leakage inductance of first inductor 110, current 208through leakage inductance of second inductor 112, magnetizing current210 of coupled inductor 120, and switching device signals 132, 134, 136,138. In this example, each of signals 132, 134, 136, 138 is assertedwhen it is in its logic-high state. However, controller 118 couldalternately be configured such that each of signals 132, 134, 136, 138is asserted when it is in its logic-low state. Controller 118 controlsfirst switching circuit 106 and second switching circuit 108 as follows.During a first sub-period 214 of switching period T₁, first switchingcircuit 106 forward biases first inductor 110, and second switchingcircuit 108 reverse biases second inductor 112, such that current 206through first inductor 110 ramps up and magnetically induces currentthrough second inductor 112. In this document, “ramps up” means toincrease in value over time, such that an ending value is greater than abeginning value. For example, in each first sub-period 214, the value ofcurrent 206 at the end up of the sub-period is greater than the value ofcurrent 206 at the beginning of the sub-period. Line segmentsrepresenting current 206 and 208 ramping up are designated as 206 u and208 u, respectively, in FIG. 2. During a second sub-period 216 of periodT₁, first switching circuit 106 reverse biases first inductor 110, andsecond switching circuit 108 reverse biases second inductor 112, suchthat current through each inductor ramps down. In this document, “rampsdown” means to decrease in value over time, such that an ending value issmaller than a beginning value. For example, in each second sub-period216, the value of current 206 at the end up of the sub-period is smallerthan the value of current 206 at the beginning of the sub-period. Linesegments representing current 206 and 208 ramping down are designated as206 d and 208 d, respectively, in FIG. 2. In first sub-period 214 ofperiod T₂, second inductor 112 is forward biased in place of firstinductor 110, and first inductor 110 is reverse biased in place ofsecond inductor 112. Periods T₁ and T₂ repeat in an alternating manner.Magnetizing current 210 has a peak-to-peak magnitude 212, and currents206 and 208 have differing magnitudes in each period T due to imperfectmagnetic coupling of first and second inductors 110, 112.

FIG. 3 is a graph 300 like graph 200 of FIG. 2, but illustratingoperation of DC-to-DC converter 100 in DCM instead of in CCM. Controller118 controls first switching circuit 106 and second switching circuit108 as follows in DCM. During a first sub-period 314 of period T, firstswitching circuit 106 forward biases first inductor 110, and secondswitching circuit 108 reverse biases second inductor 112, such thatcurrent 206 through first inductor 110 ramps up and magnetically inducescurrent through second inductor 112. Thus, controller 118 causes anenergy transfer pulse, i.e., forward biasing of first inductor 110, tooccur in first sub-period 314. First switching circuit 106 then reversebiases first inductor 110, and second switching circuit 108 reversebiases second inductor 112, in a second sub-period 316 of period T.Consequently, current 206 through first inductor 110 and current 208through second inductor 112 ramp down during second sub-period 316.

Importantly, and in contrast to conventional DCM techniques, controller118 causes an additional energy transfer pulse to occur in each DCMswitching period T. In particular, in response to magnitude of current208 through second inductor 112 falling to zero, second switchingcircuit 108 forward biases second inductor 112 in a third sub-period 318of period T, such that magnitude of current 208 through second inductor112 ramps up and magnetically induces current through first inductor110. Thus, first inductor 110 and second inductor 112 are forward biasednon-simultaneously during each DCM switching period T, i.e., duringfirst sub-period 314 and third sub-period 318, respectively. Asdiscussed below, the extra energy transfer pulse during each DCMswitching period T, i.e., forwarding biasing of second inductor 112 inthird sub-period 318, increases the ratio of transferred power tomagnetic core losses, thereby promoting high efficiency at light load.

First switching circuit 106 reverse biases first inductor 110, andsecond switching circuit 108 reverse biases second inductor 112, in afourth sub-period 320 of period T, such that current 206 through firstinductor 110 and current 208 through second inductor 112 ramp downduring fourth sub-period 320. In a fifth sub-period 322 of period T,each of first switching circuit 106 and second switching circuit 108operates in a high-impedance state to electrically isolate itsrespective inductor 110, 112, such that magnitude of current 206 throughfirst inductor 110 and magnitude of current 208 through second inductor112 each remain at zero for the duration of fifth sub-period 322.Magnetizing current 210 has a peak-to-peak magnitude 312 during DCM inDC-to-DC converter 100.

To help appreciate how the additional energy transfer pulse during DCMin DC-to-DC converter 100 helps achieve high efficiency, consider FIG.4, which includes a graph 400 like graph 300 of FIG. 3, but withDC-to-DC converter 100 modified so that only a single energy transferpulse occurs in each period. Energy is transferred from electric powersource 124 to a load connected to output port 104 only once during eachperiod T, i.e., during a first sub-period 414. However, peak-to-peakmagnetizing current 412 is similar to peak-to-peak magnetizing current212 of CCM (and peak-to-peak magnetizing current 312 of DCM in FIG. 3),and magnetic core losses increase with increasing peak-to-peakmagnetizing current. Consequently, the ratio of transferred power tomagnetic core losses is relatively low in the FIG. 4 modifiedconfiguration. In DCM as illustrated in FIG. 3 in contrast, energy istransferred from electric power source 124 to a load connected to outputport 104 twice during each period T, i.e., during first sub-period 314and during third sub-period 318. Additionally, peak-to-peak magnetizingcurrent 312 is about the same as peak magnetizing current 412 of FIG. 4.Consequently, DC-to-DC converter 100 will have a much larger ratio oftransferred power to magnetic core losses than the FIG. 4 modifiedconfiguration, and DC-to-DC converter 100 will therefore have asignificantly higher efficiency during DCM than the FIG. 4 modifiedconfiguration.

DC-to-DC converter 100 can be modified to have a different switchingpattern in DCM as long as second inductor 112 is forward biased duringeach period T while current is still flowing through at least one offirst inductor 110 and second inductor 112 after reverse biasing firstinductor 110. For example, FIG. 5 illustrates DCM of an alternateembodiment of DC-to-DC converter 100 where controller 118 causes secondswitching circuit 108 to forward bias second inductor 112 in response tofirst switching circuit 106 reverse biasing first inductor 110, insteadof in response to current 208 through second inductor 112 falling tozero. The FIG. 5 alternate embodiment will have a higher ratio oftransferred power to magnetic core losses than the FIG. 1 embodiment,but the FIG. 5 alternate embodiment will have a larger ripple currentmagnitude than the FIG. 1 embodiment.

In some other alternate embodiments of DC-to-DC converter 100, secondinductor 112 is forward biased in DCM at a time other than when firstinductor 110 is reverse biased or when current 208 through secondinductor 112 falls to zero, such as to optimize efficiency forparticular operating conditions and/or DC-to-DC convertercharacteristics. For example, FIG. 6 illustrates DCM of an alternateembodiment of DC-to-DC converter 100 where controller 118 causes secondswitching circuit 108 to forward bias second inductor 112 at time t,where time t occurs after first switching circuit 106 reverse biasesfirst inductor 110 but before current 208 through second inductor 112falls to zero.

Each period T has the same switching pattern during DCM in DC-to-DCconverter 100. However, DC-to-DC converter 100 can be modified toalternate forward biasing of inductors from one period T to the next.For example, FIG. 7 illustrates DCM of an alternate embodiment ofDC-to-DC converter 100 where a first period T₁ has a switching patternlike that illustrated in FIG. 3, but where a second period T₂ has aswitching pattern as follows. During a first sub-period 314 of periodT₂, second switching circuit 108 forward biases second inductor 112, andfirst switching circuit 106 reverse biases first inductor 110, such thatcurrent 208 through second inductor 112 ramps up and magneticallyinduces current through first inductor 110. Second switching circuit 108then reverse biases second inductor 112, and first switching circuit 106reverse biases first inductor 110, in a second sub-period 316 of periodT₂. Consequently, current 206 through first inductor 110 and current 208through second inductor 112 ramp down during second sub-period 316. Inresponse to magnitude of current 206 through first inductor 110 fallingto zero, first switching circuit 106 forward biases first inductor 110in a third sub-period 318 of period T₂, such that magnitude of current206 through first inductor 110 ramps up and magnetically induces currentthrough second inductor 112.

First switching circuit 106 reverse biases first inductor 110, andsecond switching circuit 108 reverse biases second inductor 112, in afourth sub-period 320 of period T₂, such that current 206 through firstinductor 110 and current 208 through second inductor 112 ramp downduring fourth sub-period 320. In a fifth sub-period 322 of period T₂,each of first switching circuit 106 and second switching circuit 108operates in a high-impedance state to electrically isolate itsrespective inductor 110, 112, such that magnitude of current 206 throughfirst inductor 110 and magnitude of current 208 through second inductor112 remain at zero for the duration of fifth sub-period 322. Periods T₁and T₂ repeat in an alternating manner such that the respective roles offirst and second inductors 110 and 112 alternate between successiveswitching periods. Accordingly, in this embodiment, controller 118 canbe considered to designate one of inductors 110 and 112 as the “first”inductor in each switching period and change which inductor isdesignated as the “first” inductor between successive switching periods.The alternate embodiments of FIGS. 5 and 6 could also be modified toalternate forward biasing of inductors from one period T to the next.

The concept of including more than one energy transfer pulse in each DCMswitching period can be extended to DC-to-DC converters with more thantwo phases. For example, FIG. 8 illustrates a DC-to-DC converter 800which is similar to DC-to-DC converter 100 of FIG. 1, but includes twoadditional phases 122(3) and 122(4). Phase 122(3) includes a thirdswitching circuit 848 electrically connected between input port 102 anda third switching node V_(x3), as well as a third inductor 850electrically connected between third switching node V_(x3) and commonoutput node V_(o). Phase 122(4) includes a fourth switching circuit 852electrically connected between input port 102 and a fourth switchingnode V_(x4), as well as a fourth inductor 854 electrically connectedbetween fourth switching node V_(x4) and common output node V_(o). Eachof first inductor 110, second inductor 112, third inductor 850, andfourth inductor 854 are magnetically coupled to each other to achievemutual magnetic coupling. In this document, the term “mutual magneticcoupling” means that each inductor is magnetically coupled to each otherinductor. Accordingly, each inductor 110, 112, 850, 854 includes arespective leakage inductance, and there is a respective magnetizinginductance associated with magnetic coupling of each pair of inductors110, 112, 850, 854. Third switching circuit 848 includes a controlswitching device 128(3) and a freewheeling switching device 130(3), andfourth switching circuit 852 includes a control switching device 128(4)and a freewheeling switching device 130(4). A controller 818 generatessignals 132, 134, 136, 138, 856, 858, 860, 862 to control switchingdevices 128(1), 130(1), 128(2), 132(2), 128(3), 130(3), 128(4), 130(4),respectively.

Controller 818 is similar to controller 118 of FIG. 1, and controller818 is configured to control each of first switching circuit 106, secondswitching circuit 108, third switching circuit 848, and fourth switchingcircuit 852 in DCM, as described below and as illustrated in FIG. 9.FIG. 9 includes a graph 900 illustrating operation of DC-to-DC converter800 during DCM, where vertical axis 902 represents magnitude andhorizontal axis 904 represents time. Graph 900 includes curvesrepresenting current 206 through leakage inductance of first inductor110, current 208 through leakage inductance of second inductor 112,current 864 through leakage inductance of third inductor 850, current866 through leakage inductance of fourth inductor 854, and switchingdevice signals 132, 134, 136, 138, 856, 858, 860, 862. The curvesrepresenting current 208 through leakage inductance of second inductor112, current 864 through leakage inductance of third inductor 850, andcurrent 866 through leakage inductance of fourth inductor 854 areessentially the same and are therefore represented by a single dashedline in FIG. 9 to promote illustrative clarity.

During a first sub-period 914 of period T, first switching circuit 106forward biases first inductor 110, and second, third, and fourthswitching circuits 108, 848, and 852 reverse bias second inductor 112,third inductor 850, and fourth inductor 854, respectively, such thatcurrent 206 through first inductor 110 ramps up and magnetically inducescurrent through each of second, third, and fourth inductors 112, 850,854. Each switching circuit 106, 108, 848, 852 reverse biases itrespective inductor 110, 112, 850, 854 in a second sub-period 916 ofperiod T, such that current through each inductor ramps down.

In response to magnitude of current through at least one of secondinductor 112, third inductor 850, or fourth inductor 854 falling tozero, each of second switching circuit 108, third switching circuit 848,and fourth switching circuit 852 forward biases its respective inductor112, 850, 854, in a third sub-period 918 of period T. As a result,magnitude of current through second inductor 112, third inductor 850,and fourth inductor 854 ramps up and magnetically induces currentthrough first inductor 110. Thus, first inductor 110 and second inductor112 are forward biased non-simultaneously during each DCM switchingperiod T. Additionally, first inductor 110 and third inductor 850 areforward biased non-simultaneously during each DCM switching period T,and first inductor 110 and fourth inductor 854 are also forward biasednon-simultaneously during each DCM switching period T. Each switchingcircuit 106, 108, 848, 852 then reverse biases it respective inductor110, 112, 850, 854 in a fourth sub-period 920 of period T, such thatcurrent through each inductor ramps down. In a fifth sub-period 922 ofperiod T, each switching circuit 106, 108, 848, 852 operates in ahigh-impedance state to electrically isolate its respective inductor110, 114, 850, 854, such that magnitude of current through each inductorremains at zero for the duration of fifth sub-period 922.

Controller 818 is further configured in DC-to-DC converter 800 toalternate forwarding biasing of inductors 110, 112, 850, 854 from oneperiod to the next. For example, second inductor 112 may be forwardbiased during first sub-period 914 in a period T immediately after theperiod T illustrated in FIG. 9. Accordingly, in this embodiment,controller 818 can be considered to designate one of inductors 110, 112,850, and 854 as the “first” inductor in each switching period and changewhich inductor is designated as the “first” inductor between successiveswitching periods.

Controller 818 could be modified so that it causes third sub-period 918to begin at a different time than that illustrated in FIG. 9, as long asthird sub-period 918 begins while current is still flowing through atleast one of inductors 110, 112, 850, and 854 after reverse biasingfirst inductor 110. Additionally, the switching patterns, as well asmagnetic coupling of inductors 110, 112, 850, 854, may be varied withoutdeparting from the scope hereof, as long as at least two energy transferpulses occur in each period during DCM. For example, FIG. 10 includes agraph 1000 like graph 900 of FIG. 9 but illustrating DCM of an alternateembodiment of DC-to-DC converter 800 with different magnetic coupling ofinductors 110, 112, 850, 854. In particular, inductors 110, 112, 850,854 have a “neighbor” magnetic coupling configuration, as symbolicallyillustrated in FIG. 11 where arrows 1102 represent strong magneticcoupling, in the FIG. 10 alternate embodiment. For example, althoughinductors 110, 112, 850, and 854 are all magnetically coupled, thirdinductor 850 is more strongly magnetically coupled to each of secondinductor 112 and fourth inductor 854 than to first inductor 110. Asanother example, fourth inductor 854 is more strongly magneticallycoupled to first inductor 110 and third inductor 850 than to secondinductor 112. Neighbor magnetic coupling can be more generally describedin the case of N inductors that are mutually magnetically coupled butwith inductor i being more strongly magnetically coupled to inductorsi−1 and i+1 than to the other inductors, where i=(1, 2, . . . N), withexceptions for i=1 and for i=N. In the case of i=1, inductor i is morestrongly magnetically coupled to inductor N and inductor 2 than to theother inductors, and in the case of i=N, inductor i is more stronglymagnetically coupled to inductor N−1 and inductor 1 than to the otherinductors. The curves representing current 208 through leakageinductance of second inductor 112 and current 866 through leakageinductance of fourth inductor 854 are essentially the same and aretherefore represented as a single dashed line in FIG. 10 to promoteillustrative clarity

Controller 818 is configured to control each of first switching circuit106, second switching circuit 108, third switching circuit 848, andfourth switching circuit 852 in DCM, as described below and asillustrated in FIG. 10, in the alternate embodiment of FIGS. 10 and 11.During a first sub-period 1014 of period T, first switching circuit 106forward biases first inductor 110, and second, third, and fourthswitching circuits 108, 848, and 852 reverse bias second inductor 112,third inductor 850, and fourth inductor 854, respectively, such thatcurrent 206 through first inductor 110 ramps up and magnetically inducescurrent through each of second, third, and fourth inductors 112, 850,854. Each switching circuit 106, 108, 848, 852 reverse biases itrespective inductor 110, 112, 850, 854 in a second sub-period 1016 ofperiod T, such that current through each inductor ramps down.

In response to magnitude of current 864 through third inductor 850falling to zero, third switching circuit 848 forward biases thirdinductor 850 in a third sub-period 1018 of period T. As a result,magnitude of current through third inductor 850 ramps up andmagnetically induces current each other inductor 110, 112, 854. Eachswitching circuit 106, 108, 848, 852 then reverse biases it respectiveinductor 110, 112, 850, 854 in a fourth sub-period 1020 of period T,such that current through each inductor ramps down. In a fifthsub-period 1022 of period T, each of second switching circuit 108 andfourth switching circuit 852 forward biases second inductor 112 andfourth inductor 854, respectively, such that current through secondinductor 112 and fourth inductor 854 ramps up and magnetically inducescurrent through first inductor 110 and third inductor 850. Thus, firstinductor 110, second inductor 112, and third inductor 850 are forwardbiased non-simultaneously during each DCM switching period T, and firstinductor 110, third inductor 850, and fourth inductor 854 are alsoforward biased non-simultaneously during each DCM switching period T. Ina sixth sub-period 1024 of period T, each switching circuit 106, 108,848, 852 reverse biases it respective inductor 110, 112, 850, 854, suchthat current through each inductor ramps down. In a seventh sub-period1026 of period T, each switching circuit 106, 108, 848, 852 operates ina high-impedance state to electrically isolate its respective inductor110, 114, 850, 854, such that magnitude of current through each inductorremains at zero for the duration of seventh sub-period 1026. In somealternate embodiments, third sub-period 1018 and/or fifth sub-period1022 begin at a different time than that illustrated in FIG. 10, as longas third sub-period 1018 and fifth sub-period 1022 begin while currentis still flowing through at least one of inductors 110, 112, 850, and854 after reverse biasing first inductor 110.

FIG. 12 includes a graph 1200 like that of FIG. 9 but illustrating DCMof another alternate embodiment of DC-to-DC converter 800 with differentmagnetic coupling of inductors 110, 112, 850, 854. In particular,inductors 110, 112, 850, 854 have a “ladder” magnetic couplingconfiguration, as symbolically illustrated in FIG. 13 where arrows 1302represent strong magnetic coupling, in the FIG. 12 alternate embodiment.Ladder magnetic coupling can be more generally described in the case ofN inductors as all inductors being magnetically coupled but withinductor j being more strongly magnetically coupled to inductors j−1 andj+1 than to the other inductors, where i=(1, 2, . . . N), withexceptions for cases where j=1 and where j=N. In the case of j=1,inductor j is more strongly magnetically coupled to inductor 2 than tothe other inductors, and in the case of j=N, inductor j is more stronglymagnetically coupled to inductor N−1 than to the other inductors.

Controller 818 is configured to control each of first switching circuit106, second switching circuit 108, third switching circuit 848, andfourth switching circuit 852 in DCM, as described below and asillustrated in FIG. 12, in the alternate embodiment of FIGS. 12 and 13.During a first sub-period 1214 of period T, first switching circuit 106forward biases first inductor 110, and second, third, and fourthswitching circuits 108, 848, and 852 reverse bias second inductor 112,third inductor 850, and fourth inductor 854, respectively, such thatcurrent 206 through first inductor 110 ramps up and magnetically inducescurrent through each of second, third, and fourth inductors 112, 850,854. Each switching circuit 106, 108, 848, 852 reverse biases itrespective inductor 110, 112, 850, 854 in a second sub-period 1216 ofperiod T, such that current through each inductor ramps down.

In response to magnitude of current through fourth inductor 854 fallingto zero, fourth switching circuit 852 forward biases fourth inductor 854in a third sub-period 1218 of period T. As a result, magnitude ofcurrent through fourth inductor 854 ramps up and magnetically inducescurrent through each other inductor 110, 112, 850. Each switchingcircuit 106, 108, 848, 852 then reverse biases it respective inductor110, 112, 850, 854 in a fourth sub-period 1220 of period T, such thatcurrent through each inductor ramps down. In a fifth sub-period 1222 ofperiod T, each of second switching circuit 108 and third switchingcircuit 848 forward biases second inductor 112 and third inductor 850,respectively, such that current through second inductor 112 and currentthrough third inductor 850 ramps up and magnetically induces currentthrough first inductor 110 and fourth inductor 854. Thus, first inductor110, second inductor 112, and fourth inductor 854 are forward biasednon-simultaneously during each DCM switching period T, and firstinductor 110, third inductor 850, and fourth inductor 854 are alsoforward biased non-simultaneously during each DCM switching period T. Ina sixth sub-period 1224 of period T, each switching circuit 106, 108,848, 852 reverse biases it respective inductor 110, 112, 850, 854, suchthat current through each inductor ramps down. In a seventh sub-period1226 of period T, each switching circuit 106, 108, 848, 852 operates ina high-impedance state to electrically isolate its respective inductor110, 114, 850, 854, such that magnitude of current through each inductorremains at zero for the duration of seventh sub-period 1226. In somealternate embodiments, third sub-period 1218 and/or fifth sub-period1222 begin at a different time than that illustrated in FIG. 12, as longas third sub-period 1218 and fifth sub-period 1222 begin while currentis still flowing through at least one of inductors 110, 112, 850, and854 after reverse biasing first inductor 110.

While DC-to-DC converter 800 illustrated herein as having four phases122, DC-to-DC converter 800 could be modified to have a different numberof phases 122 with appropriate changes to its switching patterns, aslong as at least two energy transfer pulses occur in each period duringDCM. Thus, DC-to-DC converter 800 can be more generally described ashaving N phases with mutual, neighbor or ladder magnetic coupling ofinductors of the phase, where N is an integer greater than two, and atleast two energy transfer pulses occur in each period during DCM.Additionally, although each of DC-to-DC converters 200 and 800 isillustrated as being a multi-phase buck converter, either DC-to-DCconverter could be modified to have a different topology, such as aboost topology or a buck-boost topology, without departing from thescope hereof.

FIG. 14 illustrates a method 1400 for discontinuous conduction modeoperation of a multi-phase DC-to-DC converter. Method 1400 begins with astep 1402 of forward biasing a first inductor magnetically coupled to asecond inductor such that current through the first inductor ramps upand magnetically induces current through the second inductor. In oneexample of step 1402, first switching circuit 106 forward biases firstinductor 110, and second switching circuit 108 reverse biases secondinductor 112, such that current 206 through first inductor 110 ramps upand magnetically induces current 208 through second inductor 112, asillustrated in FIG. 3. In step 1404, the first inductor is reversebiased after forward biasing the first inductor. In one example of step1404, first switching circuit 106 reverse biases first inductor 110while second switching circuit 108 reverse biases second inductor 112.

Step 1404 proceeds to step 1406 where the second inductor is forwardbiased such that current through the second inductor ramps up andmagnetically induces current through the first inductor, while reversebiasing the first inductor and before magnitude of current through thefirst inductor falls to zero. In one example of step 1406, secondswitching circuit 108 forward biases second inductor 112 while firstswitching circuit 106 reverse biases first inductor 110, such thatmagnitude of current 208 through second inductor 112 ramps up andmagnetically induces current through first inductor 110. In step 1408,each of the first and second inductors is reversed biased such thatmagnitude of current through each of the first and second inductorsramps down to zero. In one example of step 1408, first switching circuit106 reverse biases first inductor 110, and second switching circuit 108reverse biases second inductor 112, such that current 206 through firstinductor 110 and current 208 through second inductor 112 ramp down.

In step 1410, each of the first and second inductors is electricallyisolated such that magnitude of current through each of the first andsecond inductors remains at zero for a finite amount of time. In oneexample of step 1410, each of first switching circuit 106 and secondswitching circuit 108 operates in a high-impedance state to electricallyisolate its respective inductor 110, 112, such that magnitude of current206 through first inductor 110 and magnitude of current 208 throughsecond inductor 112 each remain at zero. Steps 1402 through 1410optionally repeat one or more times as indicated by arrow 1412.

Combinations of Features

Features described above may be combined in various ways withoutdeparting from the scope hereof. The following examples illustrate somepossible combinations:

(A1) A method for discontinuous conduction mode operation of amulti-phase DC-to-DC converter may include the steps of (1) forwardbiasing a first inductor being magnetically coupled to a second inductorsuch that a magnitude of current through the first inductor ramps up,(2) reverse biasing the first inductor after forward biasing the firstinductor, and (3) while reverse biasing the first inductor and beforethe magnitude of current through the first inductor falls to zero,forward biasing the second inductor such that a magnitude of currentthrough the second inductor ramps up.

(A2) The method denoted as (A1) may further include, after the step offorward biasing the second inductor, reverse biasing each of the firstand second inductors such that the magnitude of the current through thefirst inductor and the magnitude of the current through the secondinductor ramps down towards zero.

(A3) The method denoted as (A2) may further include, after the step ofreverse biasing each of the first and second inductors, electricallyisolating each of the first and second inductors such that the magnitudeof current through the first inductor and the magnitude of currentthrough the second inductor remains substantially at zero for a finiteamount of time.

(A4) Any of the methods denoted as (A1) through (A3) may further include(1) designating one inductor of a plurality of inductors of themulti-phase DC-to-DC converter as the first inductor in each switchingperiod of the multi-phase DC-to-DC converter and (2) changing whichinductor of the plurality of inductors is designated as the firstinductor between successive switching periods of the multi-phaseDC-to-DC converter.

(A5) In any one of the methods denoted as (A1) through (A4), theDC-to-DC converter may include at least one additional inductormagnetically coupled to each of the first and second inductors, and thestep of forward biasing the second inductor may include forwardingbiasing the second inductor while current is still flowing through atleast one of the first inductor, the second inductor, and the at leastone additional inductor, after the step of forward biasing the firstinductor.

(A6) Any one of the methods denoted as (A1) through (A4) may furtherinclude (1) forward biasing a third inductor while forward biasing thesecond inductor, where the third inductor is magnetically coupled toeach of the first and second inductors and the third inductor is morestrongly magnetically coupled to the second inductor than to the firstinductor, and (2) while reverse biasing the first inductor but beforeforward biasing the second and third inductors, forward biasing a fourthinductor, wherein the fourth inductor is magnetically coupled to each ofthe first, second, and third inductors and the fourth inductor is morestrongly magnetically coupled to the third inductor than to each of thefirst and second inductors, such that a magnitude of current flowingthrough the fourth inductor ramps up.

(A7) Any one of the methods denoted as (A1) through (A6) may furtherinclude forward biasing the second inductor in response to the magnitudeof current through the second inductor falling to zero.

(A8) Any one of the methods denoted as (A1) through (A6) may furtherinclude forward biasing the second inductor in response to the firstinductor being reverse biased.

(A9) Any one of methods denoted as (A1) through (A8) may further includesumming current through each of the first and second inductors at acommon node.

(A10) The method denoted as (A9) may further include capacitivelyfiltering the common node.

(B1) A method for discontinuous conduction mode operation of amulti-phase DC-to-DC converter including a plurality of magneticallycoupled inductors may include forward biasing at least two of theplurality of magnetically coupled inductors non-simultaneously duringeach switching period, during discontinuous conduction mode operation ofthe multi-phase DC-to-DC converter.

(C1) A multi-phase DC-to-DC converter being configured to operate in atleast a discontinuous conduction mode may include (1) a first inductormagnetically coupled to a second inductor, (2) a first switching circuitelectrically connected to the first inductor, (3) a second switchingcircuit electrically connected to the second inductor, and (4) acontroller being configured to (i) cause the first switching circuit toforward bias the first inductor such that a magnitude of current throughthe first inductor ramps up, (ii) cause the first switching circuit toreverse bias the first inductor after forward biasing the firstinductor, and (iii) cause the second switching circuit to forward biasthe second inductor such that a magnitude of current through the secondinductor ramps up, while causing the first switching circuit to reversebias the first inductor but before the magnitude of current through thefirst inductor falls to zero.

(C2) In the multi-phase DC-to-DC converter denoted as (C1), thecontroller may be further configured to cause the first and secondswitching circuits to reverse bias the first and second inductors,respectively, such that the magnitude of current through the firstinductor and the magnitude of current through the second inductor fallto zero.

(C3) In the multi-phase DC-to-DC converter denoted as (C2), thecontroller may be further configured to cause the first and secondswitching circuits to electrically isolate the first and secondinductors, respectively, such that the magnitude of current through thefirst inductor and the magnitude of current through the second inductorremain at zero for a finite amount of time.

(C4) Any one of the multi-phase DC-to-DC converters denoted as (C1)through (C3) may further include at least one additional inductor beingmagnetically coupled to at least one of the first inductor and thesecond inductor.

(C5) Any one of the multi-phase DC-to-DC converters denoted as (C1)through (C4) may further include (1) a third inductor magneticallycoupled to each of the first and second inductors, (2) a fourth inductormagnetically coupled to each of the first, second, and third inductors,(3) a third switching circuit electrically connected to the thirdinductor, and (4) a fourth switching circuit electrically connected tothe fourth inductor, where the controller is further configured to (i)cause the third switching circuit to forward bias the third inductorwhile causing the second switching circuit to forward bias the secondinductor, such that a magnitude of current through the third inductormagnetically induces current through the first inductor, and (ii) causethe fourth switching circuit to forward bias the fourth inductor whilecausing the second switching circuit to forward bias the secondinductor, such that current through the fourth inductor magneticallyinduces current through the first inductor.

(C6) Any one of the multi-phase DC-to-DC converters denoted as (C1)through (C4) may further include (1) a third inductor magneticallycoupled to each of the first and second inductors, wherein the thirdinductor is more strongly magnetically coupled to the second inductorthan to the first inductor, (2) a fourth inductor magnetically coupledto each of the first, second, and third inductors, where the fourthinductor is more strongly magnetically coupled to each of the first andthird inductors than to the second inductor, (3) a third switchingcircuit electrically connected to the third inductor, and (4) a fourthswitching circuit electrically connected to the fourth inductor, wherethe controller is further configured to (i) cause the third switchingcircuit to forward bias the third inductor, while causing the firstswitching circuit to reverse bias the first inductor but before causingthe second switching circuit to forward bias the second inductor, and(ii) cause the fourth switching circuit to forward bias the fourthinductor while causing the second switching circuit to forward bias thesecond inductor.

(C7) Any one of the multi-phase DC-to-DC converters denoted as (C1)through (C4) may further include (1) a third inductor magneticallycoupled to each of the first and second inductors, where the thirdinductor is more strongly magnetically coupled to the second inductorthan to the first inductor, (2) a fourth inductor magnetically coupledto each of the first, second, and third inductors, wherein the fourthinductor is more strongly magnetically coupled to the third inductorthan to each of the first and second inductors, (3) a third switchingcircuit electrically connected to the third inductor, (4) a fourthswitching circuit electrically connected to the fourth inductor, andwhere the controller is further configured to (i) cause the thirdswitching circuit to forward bias the third inductor while causing thesecond switching circuit to forward bias the second inductor, and (ii)cause the fourth switching circuit to forward bias the fourth inductor,while causing the first switching circuit to forward bias the firstinductor but before causing the second switching circuit to forward biasthe second inductor.

(C8) In any one of the multi-phase DC-to-DC converters denoted as (C1)thorough (C7), the controller may be further configured to cause thesecond switching circuit to forward bias the second inductor in responseto the magnitude of current through the second inductor falling to zero.

(C9) In any one of the multi-phase DC-to-DC converters denoted as (C1)through (C7), the controller may be further configured to cause thesecond switching circuit to forward bias the second inductor in responseto the first inductor being reverse biased.

(C10) In any one of the multi-phase DC-to-DC converters denoted as (C1)through (C9), the multiphase DC-to-DC converter may have a topologyselected from the group consisting of a buck converter, a boostconverter, and a buck-boost converter.

(D1) A multi-phase DC-to-DC converter may include (1) a plurality ofmagnetically coupled inductors, (2) a respective switching circuitelectrically connected to each of the plurality of inductors, and (3) acontroller configured to control the respective switching circuitselectrically connected to each of the plurality of inductors such thatat least two of the plurality of inductors are forward biasednon-simultaneously during each switching period, during discontinuousconduction mode operation of the multi-phase DC-to-DC converter.

Changes may be made in the above DC-to-DC converters and associatedmethods without departing from the scope hereof. It should thus be notedthat the matter contained in the above description and shown in theaccompanying drawings should be interpreted as illustrative and not in alimiting sense. The following claims are intended to cover generic andspecific features described herein, as well as all statements of thescope of the present method and system, which, as a matter of language,might be said to fall therebetween.

What is claimed is:
 1. A method for discontinuous conduction modeoperation of a multi-phase DC-to-DC converter, comprising the steps of:electrically isolating each of a first inductor and a second inductorsuch that a magnitude of current through the first inductor and amagnitude of current through the second inductor remains at zero for afinite amount of time, the first inductor being magnetically coupled tothe second inductor; after electrically isolating each of the firstinductor and the second inductor, forward biasing the first inductorsuch that the magnitude of current through the first inductor ramps upfrom zero and the magnitude of current through the second inductor rampsup from zero; and before the magnitude of current through the firstinductor falls to zero after forward biasing the first inductor: reversebiasing the first inductor, and while reverse biasing the firstinductor, forward biasing the second inductor such that the magnitude ofcurrent through the second inductor ramps up and the magnitude ofcurrent through the first inductor ramps up.
 2. The method of claim 1,further comprising, after the step of forward biasing the secondinductor, simultaneously reverse biasing each of the first and secondinductors such that the magnitude of the current through the firstinductor and the magnitude of the current through the second inductorramps down towards zero.
 3. The method of claim 2, further comprising,after the step of reverse biasing each of the first and secondinductors, electrically isolating each of the first and second inductorssuch that the magnitude of current through the first inductor and themagnitude of current through the second inductor remains substantiallyat zero for a finite amount of time.
 4. The method of claim 1, wherein:the DC-to-DC converter comprises at least one additional inductormagnetically coupled to each of the first and second inductors; and thestep of forward biasing the second inductor comprises forwarding biasingthe second inductor while current is still flowing through at least oneof the first inductor, the second inductor, and the at least oneadditional inductor, after the step of forward biasing the firstinductor.
 5. The method of claim 1, further comprising: forward biasinga third inductor while forward biasing the second inductor, wherein thethird inductor is magnetically coupled to each of the first and secondinductors and the third inductor is more strongly magnetically coupledto the second inductor than to the first inductor; and while reversebiasing the first inductor but before forward biasing the second andthird inductors, forward biasing a fourth inductor, wherein the fourthinductor is magnetically coupled to each of the first, second, and thirdinductors and the fourth inductor is more strongly magnetically coupledto the third inductor than to each of the first and second inductors,such that a magnitude of current flowing through the fourth inductorramps up.
 6. The method of claim 1, further comprising forward biasingthe second inductor in response to the magnitude of current through thesecond inductor falling to zero.
 7. The method of claim 1, furthercomprising forward biasing the second inductor in response to the firstinductor being reverse biased.
 8. The method of claim 1, furthercomprising summing current through each of the first and secondinductors at a common node.
 9. The method of claim 8, further comprisingcapacitively filtering the common node.
 10. A method for discontinuousconduction mode operation of a multi-phase DC-to-DC converter includinga plurality of magnetically coupled inductors, comprising forwardbiasing at least two of the plurality of magnetically coupled inductorsnon-simultaneously during a first continuous time period where amagnitude of current through at least one of the plurality ofmagnetically coupled inductors remains at a non-zero value, aftermagnitude of current through each of the plurality of magneticallycouple inductors remains at zero for a finite amount of time, duringdiscontinuous conduction mode operation of the multi-phase DC-to-DCconverter.
 11. A multi-phase DC-to-DC converter being configured tooperate in at least a discontinuous conduction mode, comprising: a firstinductor magnetically coupled to a second inductor; a first switchingcircuit electrically connected to the first inductor; a second switchingcircuit electrically connected to the second inductor; and a controllerbeing configured to: cause the first and second switching circuits toelectrically isolate the first and second inductors, respectively, suchthat a magnitude of current through the first inductor and a magnitudeof current through the second inductor remain at zero for a finiteamount of time, after causing the first and second switching circuits toelectrically isolate the first and second inductors, respectively, causethe first switching circuit to forward bias the first inductor such thatthe magnitude of current through the first inductor ramps up from zeroand the magnitude of current through the second inductor ramps up fromzero, and before the magnitude of current through the first inductorfalls to zero after forward biasing the first inductor: cause the firstswitching circuit to reverse bias the first inductor after forwardbiasing the first inductor, and cause the second switching circuit toforward bias the second inductor such that the magnitude of currentthrough the second inductor ramps up and the magnitude of currentthrough the first inductor ramps up, while causing the first switchingcircuit to reverse bias the first inductor.
 12. The multi-phase DC-to-DCconverter of claim 11, wherein the controller is further configured tocause the first and second switching circuits to simultaneously reversebias the first and second inductors, respectively, such that themagnitude of current through the first inductor and the magnitude ofcurrent through the second inductor fall to zero.
 13. The multi-phaseDC-to-DC converter of claim 11, further comprising at least oneadditional inductor being magnetically coupled to at least one of thefirst inductor and the second inductor.
 14. The multi-phase DC-to-DCconverter of claim 11, further comprising: a third inductor magneticallycoupled to each of the first and second inductors; a fourth inductormagnetically coupled to each of the first, second, and third inductors;a third switching circuit electrically connected to the third inductor;and a fourth switching circuit electrically connected to the fourthinductor; wherein the controller is further configured to: cause thethird switching circuit to forward bias the third inductor while causingthe second switching circuit to forward bias the second inductor, suchthat a magnitude of current through the third inductor magneticallyinduces current through the first inductor, and cause the fourthswitching circuit to forward bias the fourth inductor while causing thesecond switching circuit to forward bias the second inductor, such thatcurrent through the fourth inductor magnetically induces current throughthe first inductor.
 15. The multi-phase DC-to-DC converter of claim 11,further comprising: a third inductor magnetically coupled to each of thefirst and second inductors, wherein the third inductor is more stronglymagnetically coupled to the second inductor than to the first inductor;a fourth inductor magnetically coupled to each of the first, second, andthird inductors, wherein the fourth inductor is more stronglymagnetically coupled to each of the first and third inductors than tothe second inductor; a third switching circuit electrically connected tothe third inductor; and a fourth switching circuit electricallyconnected to the fourth inductor; wherein the controller is furtherconfigured to: cause the third switching circuit to forward bias thethird inductor, while causing the first switching circuit to reversebias the first inductor but before causing the second switching circuitto forward bias the second inductor, and cause the fourth switchingcircuit to forward bias the fourth inductor while causing the secondswitching circuit to forward bias the second inductor.
 16. Themulti-phase DC-to-DC converter of claim 11, further comprising: a thirdinductor magnetically coupled to each of the first and second inductors,wherein the third inductor is more strongly magnetically coupled to thesecond inductor than to the first inductor; a fourth inductormagnetically coupled to each of the first, second, and third inductors,wherein the fourth inductor is more strongly magnetically coupled to thethird inductor than to each of the first and second inductors; a thirdswitching circuit electrically connected to the third inductor; a fourthswitching circuit electrically connected to the fourth inductor; andwherein the controller is further configured to: cause the thirdswitching circuit to forward bias the third inductor while causing thesecond switching circuit to forward bias the second inductor, and causethe fourth switching circuit to forward bias the fourth inductor, whilecausing the first switching circuit to forward bias the first inductorbut before causing the second switching circuit to forward bias thesecond inductor.
 17. The multi-phase DC-to-DC converter of claim 11,wherein the controller is further configured to cause the secondswitching circuit to forward bias the second inductor in response to themagnitude of current through the second inductor falling to zero. 18.The multi-phase DC-to-DC converter of claim 11, wherein the controlleris further configured to cause the second switching circuit to forwardbias the second inductor in response to the first inductor being reversebiased.
 19. The multi-phase DC-to-DC converter of claim 11, themultiphase DC-to-DC converter having a topology selected from the groupconsisting of a buck converter, a boost converter, and a buck-boostconverter.
 20. A multi-phase DC-to-DC converter, comprising: a pluralityof magnetically coupled inductors; a respective switching circuitelectrically connected to each of the plurality of magnetically coupleinductors; and a controller configured to control the respectiveswitching circuits electrically connected to each of the plurality ofmagnetically coupled inductors such that at least two of the pluralityof magnetically coupled inductors are forward biased non-simultaneouslyduring a first continuous time period where a magnitude of currentthrough at least one of the plurality of magnetically coupled inductorsremains at a non-zero value, after magnitude of current through each ofthe plurality magnetically couple inductors remains at zero for a finiteamount of time, during discontinuous conduction mode operation of themulti-phase DC-to-DC converter.